Distribution Theory of Runs: A Markov Chain Approach
From MaRDI portal
Publication:4314909
DOI10.2307/2290933zbMath0806.60011OpenAlexW4235909251MaRDI QIDQ4314909
Markos V. Koutras, James C. Fu
Publication date: 12 February 1995
Full work available at URL: https://doi.org/10.2307/2290933
Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Distribution theory (60E99)
Related Items
The 6666 Problem ⋮ Generalized run tests for statistical process control ⋮ A New Similarity Measure and Its Use in Determining the Number of Clusters in a Multivariate Data Set ⋮ Reliability computing method for generalized \(k\)-out-of-\(n\) system ⋮ Run and frequency quotas in a multi-state markov chain ⋮ Analytic combinatorics for computing seeding probabilities ⋮ On longest consecutive patterns in Markov chains ⋮ Context Trees, Variable Length Markov Chains and Dynamical Sources ⋮ Success runs in a sequence of exchangeable binary trials ⋮ Distributions of statistics describing concentration of runs in non homogeneous Markov-dependent trials ⋮ On discrete Gibbs measure approximation to runs ⋮ Distributions of successions of arbitrary multisets ⋮ Minimal auxiliary Markov chains through sequential elimination of states ⋮ Profust reliability of linear and circular type F and G systems having two failure criteria under Markov dependency ⋮ Multiple consecutive runs of multi-state trials: distributions of \(( k_1 , k_2 , \dots , k_\ell )\) patterns ⋮ Computing waiting time probabilities related to \((k_1, k_2, \dots, k_l)\) pattern ⋮ Statistical design of ATS-unbiased charts with runs rules for monitoring exponential time between events ⋮ Distributions of \((k_1,k_2,\dots ,k_m)\)-runs with multi-state trials ⋮ Distributions related to weak runs with a minimum and a maximum number of successes: a unified approach ⋮ Joint reliability of two consecutive-\((1, l)\) or \((2, k)\)-out-of-\((2, n)\): \(F\) type systems and its application in smart street light deployment ⋮ The distribution of extended discrete random sums and its application to waiting time distributions ⋮ Accelerated Simulation of Boltzmann-BGK Equations near the Diffusive Limit with Asymptotic-Preserving Multilevel Monte Carlo ⋮ Distribution of the number of successes in success runs of length at least \(k\) in higher-order Markovian sequences ⋮ Distributions associated with \((k_1,k_2)\) events on semi-Markov binary trials ⋮ Runs rules schemes for monitoring process variability ⋮ Waiting time for an almost perfect run and applications in statistical process control ⋮ On generalized start-up demonstration tests ⋮ On the modes of the negative binomial distribution of order k ⋮ Shortest and longest length of success runs in binary sequences ⋮ Joint distributions of numbers of runs of specified lengths in a sequence of Markov dependent multistate trials ⋮ Quantifying the uncertainty in change points ⋮ Consecutive k and Related Models—A Survey ⋮ Distributions associated with general runs and patterns in hidden Markov models ⋮ The exact distribution of overlapping counting patterns associated with a sequence of homogeneous Markov-dependent multi-state trials: An application to secon ⋮ Developments of the Markov chain approach within the distribution theory of runs. ⋮ On the joint distribution of runs in the sequence of Markov-dependent multi-state trials ⋮ On the dual reliability systems of \((n,f,k)\) and \(\langle n,f,k \rangle\) ⋮ Runs in a Bivariate Sequence Over the First Coordinate ⋮ Bonferroni-type inequalities for conditional scan statistics ⋮ Waiting time distributions of simple and compound patterns in a sequence of \(r\)th order Markov dependent multi-state trials ⋮ The distribution of the usual provider continuity index under Markov dependence ⋮ Success run statistics defined on an urn model ⋮ Corrected discrete approximations for the conditional and unconditional distributions of the continuous scan statistic ⋮ On Generating Functions of Waiting Times and Numbers of Occurrences of Compound Patterns in a Sequence of Multistate Trials ⋮ Approximation of sojourn-times via maximal couplings: motif frequency distributions ⋮ On exact and large deviation approximation for the distribution of the longest run in a sequence of two-state Markov dependent trials ⋮ Вычисление распределения одной комбинаторной статистики, заданной на последовательностях с фиксированным составом знаков ⋮ Reliability evaluation of generalised multi-statek-out-of-nsystems based on FMCI approach ⋮ Pattern Markov Chains: Optimal Markov Chain Embedding Through Deterministic Finite Automata ⋮ Distributions of Runs and Scans on Higher-Order Markov Trees ⋮ Approximate probabilities for runs and patterns in i.i.d. and Markov-dependent multistate trials ⋮ Waiting time distributions of competing patterns in higher-order Markovian sequences ⋮ On ordered series and later waiting time distributions in a sequence of Markov dependent multistate trials ⋮ Convergence theorems for the lengths of consecutive successes of Markov Bernoulli sequences ⋮ Gambling Teams and Waiting Times for Patterns in Two-State Markov Chains ⋮ Waiting Times and Number of Appearances of Runs: A Unified Approach ⋮ Digital search trees and chaos game representation ⋮ Reliabilities for (n, f, k (i, j)) and ⟨n, f, k (i, j)⟩ Systems ⋮ A Sensitivity Analysis for System Reliability ⋮ Distribution of waiting time until the \(r\)th occurrence of a compound pattern ⋮ The distributions of the frequency of occurrence of nucleotide subsequences ⋮ Design of multiple run sampling plan ⋮ On the average run lengths of quality control schemes using a Markov chain approach ⋮ Sensitivity analysis and efficient method for identifying optimal spaced seeds ⋮ On the distribution of the total number of run lengths ⋮ Joint distributions associated with patterns, successes and failures in a sequence of multi-state trials ⋮ Waiting time problems for a two-dimensional pattern ⋮ Poisson approximations for 2-dimensional patterns ⋮ Waiting time distribution for the emergence of superpatterns ⋮ A compound control chart for monitoring and controlling high quality processes ⋮ On the length and the position of the minimum sequence containing all runs of ones in a Markovian binary sequence ⋮ Weak runs in sequences of binary trials ⋮ Start-up demonstration tests with sparse connection ⋮ Application of auxiliary Markov chains to start-up demonstration tests ⋮ Joint distributions of runs in a sequence of higher-order two-state Markov trials ⋮ Range reliability in random walks ⋮ Binomial distribution of order \(k\) in a modified binary sequence ⋮ Recursive equations in finite Markov chain imbedding ⋮ Stochastic ordering among success runs statistics in a sequence of exchangeable binary trials ⋮ Faster exact distributions of pattern statistics through sequential elimination of states ⋮ On finite Markov chain imbedding and its applications ⋮ Explicit distributional results in pattern formation ⋮ Bounds for coherent reliability structures ⋮ Sooner and later waiting time problems for success and failure runs in higher order Markov dependent trials ⋮ On a waiting time distribution in a sequence of Bernoulli trials ⋮ Runs, scans and urn model distributions: A unified Markov chain approach ⋮ Some sufficient conditions for stochastic comparisons between hitting times for skip-free Markov chains ⋮ Discriminating membrane proteins using the joint distribution of length sums of success and failure runs ⋮ Reliability analysis of \(k\)-out-of-\(n\):F balanced systems with multiple functional sectors ⋮ Non-parametric randomness tests based on success runs of fixed length ⋮ Corrected discrete approximations for multiple window scan statistics of one-dimensional Poisson processes ⋮ Stochastic analysis of minimal automata growth for generalized strings ⋮ On coupon collector's and Dixie cup problems under fixed and random sample size sampling schemes ⋮ Waiting time for consecutive repetitions of a pattern and related distributions ⋮ Markov binomial distribution of order \(k\) and its applications ⋮ On success runs in a sequence of dependent trials with a change point ⋮ Generalizations of distributions related to \((k_1,k_2)\)-runs ⋮ The analysis and comparison of start-up demonstration tests ⋮ Distribution and double generating function of number of patterns in a sequence of Markov dependent multistate trials ⋮ Statistical modeling for discrete patterns in a sequence of exchangeable trials ⋮ Bivariate Fibonacci polynomials of order \(k\) with statistical applications ⋮ Exact and asymptotic results for pattern waiting times ⋮ Joint distributions of numbers of runs of specified lengths on directed trees ⋮ Chess, chance and conspiracy ⋮ Approximating the extreme right-hand tail probability for the distribution of the number of patterns in a sequence of multi-state trials ⋮ Distributions of patterns of two successes separated by a string of \(k-2\) failures ⋮ On the longest gap between power-rate arrivals ⋮ On the tail probability of the longest well-matching run. ⋮ On the distribution of the number of success runs in a continuous time Markov chain ⋮ The distribution of the length of the longest increasing subsequence in random permutations of arbitrary multi-sets ⋮ On the individuals chart with supplementary runs rules under serial dependence ⋮ Markovian start-up demonstration tests with rejection of units upon observing \(d\) failures. ⋮ Useful inequalities for the longest run distribution ⋮ Joint distributions of numbers of occurrences of a discrete pattern and weak convergence of an empirical process for the pattern ⋮ Multiple pattern matching: a Markov chain approach ⋮ Robust scan statistics for detecting a local change in population mean for normal data ⋮ Approximating the distributions of runs and patterns ⋮ Distribution of the length of the longest common subsequence of two multi-state biological sequences ⋮ Generalizations of runs and patterns distributions for sequences of binary trials ⋮ Scan statistics for normal data with outliers ⋮ Number of appearances of events in random sequences: a new generating function approach to type II and type III runs ⋮ Implied distributions in multiple change point problems ⋮ Distributions related to \((k_{1},k_{2})\) events ⋮ Distributions of numbers of runs and scans on directed acyclic graphs with generation ⋮ Distributions of simple patterns in some kinds of exchangeable sequences ⋮ On success runs of length exceeded a threshold ⋮ On average run lengths of control charts for autocorrelated processes ⋮ On the conditional and unconditional distributions of the number of success runs on a circle with applications ⋮ On the distribution and expectation of success runs in nonhomogeneous Markov dependent trials ⋮ Waiting time distributions of runs in higher order Markov chains ⋮ On success runs of a fixed length in Bernoulli sequences: exact and asymptotic results ⋮ Consecutive covering arrays and a new randomness test ⋮ On the distribution of runs of ones in binary strings ⋮ A test statistic for weighted runs ⋮ The reliability of a generalized consecutive system ⋮ Pseudo-binomial approximation to \((k_1, k_2)\)-runs ⋮ Reliability for discrete state systems with cyclic missions periods ⋮ Decoupling combinatorial complexity: a two-step approach to distributions of runs ⋮ Moments of the count of a regular expression in a heterogeneous random sequence ⋮ Time inhomogeneity in longest gap and longest run problems ⋮ On waiting time distributions associated with compound patterns in a sequence of multi-state trials ⋮ The exact distribution of the \(k\)-tuple statistic for sequence homology ⋮ Conditional waiting time distributions of runs and patterns and their applications ⋮ On the joint distribution of runs in a sequence of multi-state trials ⋮ Waiting time distribution of generalized later patterns ⋮ On the exact distributions of Eulerian and Simon Newcomb numbers associated with random permutations ⋮ The exact distribution of the continuity of care measure NOP ⋮ Bivariate Markov chain embeddable variables of polynomial type ⋮ On occurrence of subpattern and method of gambling teams ⋮ R-2 composition tests: a family of statistical randomness tests for a collection of binary sequences ⋮ Distributions of pattern statistics in sparse Markov models ⋮ On run statistics for binary trials ⋮ Reliabilities for \((n,f,k)\) systems ⋮ The distribution of increasing \(l\)-sequences in random permutations: A Markov chain approach ⋮ Length of the minimum sequence containing repeats of success runs ⋮ Formulae and recursions for the joint distributions of success runs of several lengths in a two-state Markov chain ⋮ Large deviation behavior for the longest head run in an IID Bernoulli sequence ⋮ Joint distributions of numbers of success runs of specified lengths in linear and circular se\-quences ⋮ A martingale approach to scan statistics ⋮ An algorithm to compute the probability of a run in binary fourth-order Markovian trials. ⋮ On the number of overflown urns and excess balls in an allocation model with limited urn capacity ⋮ Binary consecutive covering arrays
This page was built for publication: Distribution Theory of Runs: A Markov Chain Approach